How to fit\adjust text into given formate?

Question

I want to fit the following text into an A4 size page but the text leaks out of the given formate. So, how do i adjust it? The text is written in latex file as follows:

 $\langle W(E_{1}), V_{1}, E_{1}  \rangle \oplus \langle W(E_{2}), V_{2}, E_{2}  \rangle=\begin{cases}
\langle W(E_{1}), V_{1}, E_{1}  \rangle,~ \text{if}~ \langle W(E_{1}), V_{1}, E_{1}  \rangle \neq \langle W(E_{\infty}), V_{\infty}, E_{\infty} \rangle \\
\langle W(E_{2}),~ V_{2}, E_{2}  \rangle ~\text{Otherwise}
\end{cases} $
$\forall~\langle W(E_{1}), V_{1}, E_{1}  \rangle,~\langle W(E_{2}),~ V_{2}, E_{2}  \rangle \in S.$

Answer 1

I'd place the first part of the equation in a display math environment and insert a line break in the lengthy conditioning part of the first case.

\documentclass{article}
\usepackage{amsmath,amssymb}
\usepackage{geometry} % choose page size parameters suitably

\begin{document}

\begin{equation*}
\langle W(E_{1}), V_{1}, E_{1} \rangle \oplus 
\langle W(E_{2}), V_{2}, E_{2} \rangle =
\begin{cases}
\langle W(E_{1}), V_{1}, E_{1} \rangle,
  & \text{if } \langle W(E_{1}), V_{1}, E_{1} \rangle \\ 
  & \quad\neq \langle  W(E_{\infty}), V_{\infty}, E_{\infty} \rangle \\
\langle W(E_{2}), V_{2}, E_{2} \rangle 
  &\text{otherwise}
\end{cases}
\end{equation*}
for all $\langle W(E_{1}), V_{1}, E_{1}\rangle, 
\langle W(E_{2}), V_{2}, E_{2} \rangle \in S$.

\end{document}

Answer 2

Using \multline:

\documentclass[a4paper]{article}

\usepackage{amsmath}

\begin{document}

\begin{multline*}
  \langle W(E_1), V_1, E_1 \rangle \oplus \langle W(E_2),
  V_2, E_2 \rangle =\\
  \begin{cases}
    \langle W(E_1), V_1, E_1 \rangle & \text{if $\langle W(E_1),
    V_1, E_1 \rangle \neq \langle W(E_\infty), V_\infty,
    E_\infty \rangle$}\\
    \langle W(E_2), V_2, E_2 \rangle & \text{otherwise}
  \end{cases}
\end{multline*}
$\forall\langle W(E_1), V_1, E_1 \rangle, \langle W(E_2),
V_2, E_2 \rangle \in S$.

\end{document}